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Spherical bessel functunction help

  • Thread starter lycraa
  • Start date
  • #1
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Homework Statement


i need to derive the recurrence relations for the spherical Bessel function. i got jn-1(x)+jn+1(x)=(2n+1)/x jn(x) but i cant get njn-1(x)-(n+1)jn+1(x)=(2n+1) j'n(x). i know i have to use jn(x)=(pi/2x)1/2Jn+1/2(x) and the recurrence relations for regular bessel functions Jn-1(x)-Jn+1(x)=2 J'n(x) and possibly also Jn-1(x)+Jn+1(x)=2n/x Jn(x). i don't even know were to start because i don't know were the 'n's come from in the recurrence relation I'm trying to derive.


Homework Equations


above

The Attempt at a Solution


i just need to know were to start! nothing i've tried comes even close
 

Answers and Replies

  • #2
fzero
Science Advisor
Homework Helper
Gold Member
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Start by computing [tex]j_n'(x)[/tex] in terms of [tex]J_{n+1/2}(x)[/tex]. Use the ordinary recurrence relation to eliminate [tex]J'_{n+1/2}(x)[/tex].
 

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